A small glass bead has been charged to +19 nC. A metal ball bearing 1.0 cm above the bead feels a 0.030 N downward electric force. What is the charge on the ball bearing?
To find the charge on the ball bearing, we can use Coulomb's Law, which relates the force between two charged objects to their charges and the distance between them.
Coulomb's Law can be given as:
F = (k * |q1 * q2|) / r^2
Where:
F is the force between the objects
k is the electrostatic constant (k = 8.99 * 10^9 N m^2 / C^2)
q1 and q2 are the charges on the objects
r is the distance between the objects
In this case, the force on the ball bearing is given as 0.030 N, and the distance between the ball bearing and the charged bead is 1.0 cm (which is equivalent to 0.01 m). The charge on the bead is +19 nC, which can be written as +19 * 10^-9 C.
Substituting these values into Coulomb's Law, we can solve for the charge on the ball bearing:
0.030 N = (8.99 * 10^9 N m^2 / C^2) * |(+19 * 10^-9 C) * q2| / (0.01 m)^2
To find q2, we need to rearrange the equation:
|q2| = (0.030 N * (0.01 m)^2) / (8.99 * 10^9 N m^2 / C^2 * |(+19 * 10^-9 C)|)
|q2| = 3.0 * 10^-4 C
Since force is acting in the downward direction, the charge on the ball bearing is negative. Therefore, the charge on the ball bearing is -3.0 * 10^-4 C.